Problem: Simplify the following expression: $\sqrt{20}-\sqrt{5}+\sqrt{45}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{20}-\sqrt{5}+\sqrt{45}$ $= \sqrt{4 \cdot 5}-\sqrt{5}+\sqrt{9 \cdot 5}$ Separate the radicals and simplify. $= \sqrt{4} \cdot \sqrt{5}-\sqrt{5}+\sqrt{9} \cdot \sqrt{5}$ $= 2\sqrt{5}-\sqrt{5}+3\sqrt{5}$ Finally, simplify by combining the terms. $= ( 2 - 1 + 3 )\sqrt{5} = 4\sqrt{5}$